Problem: Simplify the following expression and state the condition under which the simplification is valid: $x = \dfrac{p^2 - p - 20}{p^2 - 5p - 36}$
Solution: First factor the expressions in the numerator and denominator. $ \dfrac{p^2 - p - 20}{p^2 - 5p - 36} = \dfrac{(p - 5)(p + 4)}{(p - 9)(p + 4)} $ Notice that the term $(p + 4)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(p + 4)$ gives: $x = \dfrac{p - 5}{p - 9}$ Since we divided by $(p + 4)$, $p \neq -4$. $x = \dfrac{p - 5}{p - 9}; \space p \neq -4$